Since the seminal paper by Marzetta from 2010, the Massive MIMO paradigm in communication systems has changed from being a theoretical scaled-up version of MIMO, with an infinite number of antennas, to a practical technology. Its key concepts have been adopted in the 5G new radio standard and base stations, where 64 fully-digital transceivers have been commercially deployed. Motivated by these recent developments, this paper considers a co-located MIMO radar with $M_T$ transmitting and $M_R$ receiving antennas and explores the potential benefits of having a large number of virtual spatial antenna channels $N=M_TM_R$ . Particularly, we focus on the target detection problem and develop a robust Wald-type test that guarantees certain detection performance, regardless of the unknown statistical characterization of the disturbance. Closed-form expressions for the probabilities of false alarm and detection are derived for the asymptotic regime $N\rightarrow \infty$ . Numerical results are used to validate the asymptotic analysis in the finite system regime with different disturbance models. Our results imply that there always exists a sufficient number of antennas for which the performance requirements are satisfied, without any a-priori knowledge of the disturbance statistics. This is referred to as the Massive MIMO regime of the radar system.

Massive MIMO Radar for Target Detection

We examine the clutter covariance matrices for ground moving-target indicator (GMTI) multiple-input, multiple-output (MIMO) radar systems, and, in particular, discuss a potential suboptimal increase in their rank This increase in rank will generically degrade the ability of a MIMO GMTI system to detect slowly moving targets We first give a general theoretical analysis and then focus on simulated and experimental data for MIMO systems employing fast-time random, time-division multiple-access (TDMA), and Doppler-division multiple-access (DDMA) waveforms We will show that for the TDMA/DDMA waveforms the clutter covariance matrix in a given Doppler bin is effectively rank 1 for both the simulated and experimental data

Clutter covariance matrices for GMTI MIMO radar

The current literature on MIMO radar commonly uses a signal model that assumes that the Doppler and delay parameters of the scatterers lie on a discrete grid. The Doppler and delay of actual scatterers take on arbitrary values causing a mismatch between this model and reality. Here, we develop a signal model that takes into account this mismatch and shows that it causes a distortion of the array manifold. This distortion, which is unique to MIMO radar, impacts the results of array processing functions such as beamforming, null steering, and direction finding. The degree of performance degradation caused by this is illustrated by numerical examples.

Effects of Model Mismatch in MIMO Radar

Coherent multiple-input multiple-output (MIMO) radar is characterized by having a transmit antenna array and a receive antenna array located in a pseudo-monostatic configuration such that desired target returns from the far-field are coherent. Each element (or subarray) of the transmit array radiates an independent, ideally orthogonal, waveform. Such a radar offers the ability to digitally form beams, possibly adaptively, on both transmit and receive within the receive signal processor. The fundamental advantages of MIMO radar over modern single-input multiple-output (SIMO) radar can be demonstrated with a multiple-input single-output (MISO) radar. A MISO radar testbed with up to four transmit channels and a single receiver was built to evaluate the various classes of MIMO waveforms. Results of these tests are presented.

MISO radar beamforming demonstration

The application of multiple-input multiple-output (MIMO) techniques to radar has been an active research topic recently due to their successful implementation in modern wireless communications systems. Looking to further leverage this success, many researchers have studied the applicability of spatial diversity and waveform diversity to radar. It has been shown that a MIMO radar system with spatially diverse transmitters and receivers utilizing orthogonal waveforms can provide benefits in target detection and parameter estimation when compared to a traditional phased array system. The current research typically attempts to apply the Swerling-I model when analyzing the performance of the multistatic MIMO system. However, this model was originally developed for monostatic systems and may not accurately describe the bistatic scattering behavior of targets. Other research has shown that MIMO arrays with co-located transmitters and receivers could be used in imaging applications by forming virtual arrays of elements. It has been suggested that time diversity be used to unambiguously separate the transmitted waveforms at the receivers. The application of suitable transmit waveforms which could be measured simultaneously and then separated by matched filtering could extend the usefulness of the virtual array idea. 
This dissertation explores MIMO concepts using both co-located and spatially diverse transmitters and receivers. A new target scattering model is presented which extends the Swerling-I model to include a new correlation parameter. This parameter allows the bistatic scattering behavior of the model to be tuned to more accurately represent some classes of real-world targets. It is shown through simulation that increasing the amount of correlation in the target effectively decreases the target detection performance of the MIMO system, so validation of these target models is necessary. 
A MIMO array with co-located antennas is also explored to study the effects of using orthogonal waveforms (or waveforms with low cross-correlations) on imaging quality. The approximation of a MIMO array by a virtual array whose elements are located at the center of mass of each transmitter/receiver pair is verified through simulation. Then images of both a point target and distributed scatterer are compared to test whether or not waveforms with small cross-correlations can be separated sufficiently in the receivers. It is shown that the separation is sufficient in both cases. 
The design and development of a flexible software-defined radar system (SDR) is outlined. Utilizing a powerful digital baseband transceiver with a 1 GSPS dual-channel ADC and DAC, the system is capable of generating, receiving, and coherently processing waveforms with up to 500 MHz of bandwidth. Two independent transmit channels and two independent receive channels are available, with a center frequency which can be tuned from 2–18 GHz. This system is used to measure the scattered fields from a complex target using spatially diverse transmitters and receivers. These results are used to evaluate the correlated scatterers model presented here. Furthermore, the SDR is used to measure a sphere using co-located transmitters and receivers to experimentally verify the imaging simulations.

Exploration of mimo radar techniques with a software-defined radar

A multiple-input, multiple-output (MIMO) radar system uses multiple, spatially diverse transmitters and receivers with separable, independent waveforms with the goal of enhancing resolution and, thus, improving performance. Key to the achievement of these performance benefits is the degree to which the transmitted waveforms may be separated on receive, e.g. the correlation properties amongst the waveforms. A previously defined correlation metric useful for designing “good” waveforms is simplified and its global minimum prescribed for M coded constant modulus waveforms each consisting of N chips and shown to be equal to M-1 (independent of the number of chips). The theory is validated using random phase waveforms as well as optimized waveforms using a previously defined iterative procedure (“CAN”), which is shown to effectively achieve the derived minimum bound. An important consequence of this large level of correlation residue for an optimal waveform set when used to perform a ground moving target indicator (GMTI) function in an airborne radar observing distributed clutter is that the rank of the resulting MIMO interference covariance is increased beyond that of an idealized orthogonal waveform set leading to significant degradation in the clutter mitigation performance, as shown through simulation. An approach to mitigating this effect through the use of partially optimized waveforms tailored to the scenario of interest is demonstrated to achieve the performance of an idealized orthogonal waveform set.

Christopher M. Teixeira

Papers

Performance bounds on MIMO radar with optimized coded constant modulus waveforms